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Estimating the surface area of non-convex particles from central planar sections

Publikation: Working paperForskning

Standard

Estimating the surface area of non-convex particles from central planar sections. / Thórisdóttir, Ólöf; H.Rafati, Ali; Kiderlen, Markus.

Centre for Stochastic Geometry and Advanced Bioimaging, Aarhus University, 2013.

Publikation: Working paperForskning

Harvard

Thórisdóttir, Ó, H.Rafati, A & Kiderlen, M 2013 'Estimating the surface area of non-convex particles from central planar sections' Centre for Stochastic Geometry and Advanced Bioimaging, Aarhus University. <http://math.au.dk/publs?publid=987>

APA

Thórisdóttir, Ó., H.Rafati, A., & Kiderlen, M. (2013). Estimating the surface area of non-convex particles from central planar sections. Centre for Stochastic Geometry and Advanced Bioimaging, Aarhus University. CSGB Research Reports Nr. 08 http://math.au.dk/publs?publid=987

CBE

Thórisdóttir Ó, H.Rafati A, Kiderlen M. 2013. Estimating the surface area of non-convex particles from central planar sections. Centre for Stochastic Geometry and Advanced Bioimaging, Aarhus University.

MLA

Thórisdóttir, Ólöf, Ali H.Rafati, og Markus Kiderlen Estimating the surface area of non-convex particles from central planar sections. Centre for Stochastic Geometry and Advanced Bioimaging, Aarhus University. (CSGB Research Reports; Journal nr. 08). 2013., 29 s.

Vancouver

Thórisdóttir Ó, H.Rafati A, Kiderlen M. Estimating the surface area of non-convex particles from central planar sections. Centre for Stochastic Geometry and Advanced Bioimaging, Aarhus University. 2013.

Author

Thórisdóttir, Ólöf ; H.Rafati, Ali ; Kiderlen, Markus. / Estimating the surface area of non-convex particles from central planar sections. Centre for Stochastic Geometry and Advanced Bioimaging, Aarhus University, 2013. (CSGB Research Reports; Nr. 08).

Bibtex

@techreport{55abc54facbc49cbba7d967b6357ae0a,
title = "Estimating the surface area of non-convex particles from central planar sections",
abstract = "In this paper, we present a new surface area estimator in local stereology. This new estimator is called the 'Morse type surface area estimator' and is obtained using a two-stage sampling procedure. First a plane section through a fixed reference point of a three-dimensional structure is taken. In this section plane a modification of the area tangent count method is used. The Morse type estimator generalizes Cruz-Orive's pivotal estimator for convex objects to non-convex objects. The advantages of the Morse type estimator over existing local surface area estimators are illustrated in a simulation study. The Morse type estimator is well suited for computer assisted confocal microscopy and we demonstrate its practicability in a biological application: the surface area estimation of the nuclei of giant-cell glioblastoma from microscopy images. We also present an interactive software that allows the user to efficiently obtain the estimator.",
keywords = "surface area, local stereology, area tangent count, invariator principle, Morse type surface area estimator",
author = "{\'O}l{\"o}f Th{\'o}risd{\'o}ttir and Ali H.Rafati and Markus Kiderlen",
year = "2013",
language = "English",
series = "CSGB Research Reports",
number = "08",
publisher = "Centre for Stochastic Geometry and Advanced Bioimaging, Aarhus University",
type = "WorkingPaper",
institution = "Centre for Stochastic Geometry and Advanced Bioimaging, Aarhus University",

}

RIS

TY - UNPB

T1 - Estimating the surface area of non-convex particles from central planar sections

AU - Thórisdóttir, Ólöf

AU - H.Rafati, Ali

AU - Kiderlen, Markus

PY - 2013

Y1 - 2013

N2 - In this paper, we present a new surface area estimator in local stereology. This new estimator is called the 'Morse type surface area estimator' and is obtained using a two-stage sampling procedure. First a plane section through a fixed reference point of a three-dimensional structure is taken. In this section plane a modification of the area tangent count method is used. The Morse type estimator generalizes Cruz-Orive's pivotal estimator for convex objects to non-convex objects. The advantages of the Morse type estimator over existing local surface area estimators are illustrated in a simulation study. The Morse type estimator is well suited for computer assisted confocal microscopy and we demonstrate its practicability in a biological application: the surface area estimation of the nuclei of giant-cell glioblastoma from microscopy images. We also present an interactive software that allows the user to efficiently obtain the estimator.

AB - In this paper, we present a new surface area estimator in local stereology. This new estimator is called the 'Morse type surface area estimator' and is obtained using a two-stage sampling procedure. First a plane section through a fixed reference point of a three-dimensional structure is taken. In this section plane a modification of the area tangent count method is used. The Morse type estimator generalizes Cruz-Orive's pivotal estimator for convex objects to non-convex objects. The advantages of the Morse type estimator over existing local surface area estimators are illustrated in a simulation study. The Morse type estimator is well suited for computer assisted confocal microscopy and we demonstrate its practicability in a biological application: the surface area estimation of the nuclei of giant-cell glioblastoma from microscopy images. We also present an interactive software that allows the user to efficiently obtain the estimator.

KW - surface area

KW - local stereology

KW - area tangent count

KW - invariator principle

KW - Morse type surface area estimator

M3 - Working paper

T3 - CSGB Research Reports

BT - Estimating the surface area of non-convex particles from central planar sections

PB - Centre for Stochastic Geometry and Advanced Bioimaging, Aarhus University

ER -